Convection due to thermal buoyancy in the gravitational field of the Earth is the overall driving mechanism of fluid flow in the interior of our planet. In particular large effort has been involved in theoretical prediction and numerical simulation of convection in both the outer core and mantle. The first is mainly responsible for the generation of a magnetic field, while the later constitutes the main cause for surface manifestations like tectonics and volcanism. Our main understanding of physical processes, which shape the interior of our planet, comes from theoretical studies, numerical simulations and laboratory experiments. While the theory determines the basic concepts, the numerical simulation is able to check approximations and modeling approaches for a rich variety of parameters. Finally, the laboratory experiments allow capturing all non-linear effects and associated instabilities without analytical and numerical simplifications.

In this project we are running numerical simulations of fluid flow as accompanying work of the Geophysical Fluid Flow under Microgravity experiment (Geoflow). The Geoflow experiment was designed in the Department for Aerodynamics and Fluid Mechanics at the Brandenburg University of Technology and its hardware was developed in cooperation with EADS Astrium. Geoflow is an ESA investigation running inside the Fluid Science Laboratory (FSL) on the ISS. The goal of the experiment is to better understand the non-linear physical processes that take place in the interior of our planet.

The GeoFlow experiment investigates the fluid motion in a gap between two concentric spheres, with the inner spherical shell heated and the outer spherical shell cooled (von Larcher, 2008), this setup being a model for the interior structure of our planet. In case of massive spherical objects like planets or stars the buoyancy force is driven by a gravitational potential. However, in an Earth laboratory the gravity is aligned with a vertical directed unit vector. To set-up a central symmetry buoyancy field, a high voltage potential and a dielectric liquid as working fluid in the spherical cavity are used. This technique to realize a self-gravitating force field experimentally requires microgravity conditions in order to reduce unidirectional influence of acceleration due to gravity dominating fluid flow in an Earth-based laboratory (Fig. 1a). For GeoFlow this specific conditions are available in the European module COLUMBUS of the International Space Station ISS (Fig 1b). While GeoFlow I used a working fluid with temperature-independent properties, its focus being convection patterns in Earth's liquid core, GeoFlow II uses a fluid which is designed to change its inherent resistance to flow (viscosity) when its temperature changes, behavior that resembles more the convection in Earth's mantle.

Figure 1: The patterns obtained using numerical simulations that follow the set-up of the GeoFow experiments: (a) superposition of two buoyancy fields ( Earth-gravitational field and the induced gravitational field) corresponding to laboratory experiments and (b) using only the central buoyancy field corresponding to an experiment performed on the ISS.

The flow visualization method used in the experiment as delivered by the Optical Diagnostics Module (ODM) of the Fluid Science Laboratory, is the so called Wollaston-Prism shearing interferometry WSI, which produces fringe pattern images (Futterer et al., 2012). This measurement technique is sensitive to variation of the refractive index which describes how light propagates through a medium. The refractive index is sensitive to density gradients which are caused by temperature changes. Therefore if the refractive index of a medium changes due to convection, light waves passing the measurement section experience a phase shift and interference phenomena result. In images, called interferograms, these interference phenomena become visible as fringes. Using the fringe patterns caused by the temperature gradients, global scale convection patterns can be reproduced (Fig. 2).

Additional to the experiments, numerical simulations in a 3D spherical geometry have been carried out to reproduce the results obtained in the GeoFlow experiments. By comparing the numerical simulations with the experiment data, we are able to verify the validity of our computer models and expand the parameter space to ranges not applicable for an experiment.